Particles with a diameter of 100 nm or less are generally called nanoparticles, and are just beginning to be used in various fields because they have properties different from those of general bulk materials of even the same material. Various methods such as the laser diffraction/scattering method have been known as the method for measuring the particle size. Among them, methods based on the so-called dynamic scattering method (the photon correlation method) have been employed mainly for nanoparticles with a diameter of 100 nm or less (refer to Patent Literatures 1 and 2, for example).
The dynamic scattering method utilizes the Brownian motion of the particles. According to the method, particles performing a Brownian motion in a medium are exposed to a light beam, the intensity of scattered light from the particles is measured at a predetermined position, the fluctuation of the scattered light intensity caused by the Brownian motion of the particles, that is, the temporal change in the scattered light is captured, and the particle size distribution of the particles to be measured is calculated by utilizing the fact that particles each perform a Brownian motion with the intensity according to its particle size.
However, in the dynamic scattering method (the photon correlation method) in which the fluctuation of scattered light from the particles is measured, the fluctuation of the scattered light to be measured is imperceptible in the case of microparticles because the intensity of the scattered light from the microparticles is proportional to the fifth to sixth power of the particle size. Due to its principle, the problems of poor measurement sensitivity as well as poor S/N cannot be avoided.
As a powerful approach for solving such unavoidable problems in the dynamic scattering method, there has been proposed a method and an apparatus for electrophoresing particles dispersed movably in a medium by applying a spatially periodic electric field to the particles, generating a quasi-diffraction grating by making the particles have a spatially periodic alteration in concentration, in this state, detecting diffracted light obtained by exposing the particles to a parallel light flux such as a laser beam, and calculating the diffusion coefficient and the size of the particles from the temporal change in the diffracted light after stopping the application of the electric field (refer to Patent Literature 3).
The method and the apparatus proposed above utilize dielectrophoresis or electrophoresis of the particles in the medium, and utilizes the fact that, from the state where a diffraction grating resulting from concentration distribution (density distribution) of the particles is generated by applying an electric field, the annihilation process of the diffraction grating by stopping the application of the electric field depends on the diffusion coefficient of the particles. The diffusion coefficient and therefore the size of the particles can be calculated from the time required for dissipation of diffracted light from the diffraction grating resulting from the density distribution of the particles.
In the measurement method and the apparatus described above, the diffraction grating resulting from the density distribution of the particles is formed in the vicinity of an electrode pair for applying the electric field to the sample to induce the dielectrophoresis of the particles. An electrode pattern with which diffracted light from the electrode pair and the diffracted light from the diffraction grating resulting from the density distribution of the particles can be separately measured is also proposed (refer to Patent Literature 4, for example).
That is, each of electrodes constituting the electrode pair includes multiple mutually parallel linear electrode pieces and a connection part electrically connecting the respective electrode pieces to each other. Each electrode has a pattern that electrode piece ununiformly-arranged areas including at least two linear electrode pieces arranged adjacently to each other, and electrode piece absent areas with no electrode piece arranged therein are formed alternately. The electrode pairs are formed by arranging the electrodes so that the electrode piece ununiformly-arranged areas of one electrode are positioned in the electrode piece absent areas of the other electrode respectively, and the electrode pieces are arranged in parallel with each other.
With the configuration above, when a voltage is applied to between the electrode pieces, high-density areas of the particles are formed only in a part where the electrode pieces of one electrode are adjacent to the electrode pieces of the other electrode. Thus, a grating pitch of the diffraction grating resulting from the density distribution of the particles is larger than a pitch of the electrode pieces. Thereby, the diffracted light of the specific order from the diffraction grating resulting from the density distribution of the particles, such as the diffracted light of the [2m+1]th order (m is an integer) in the case where two electrode pieces are ununiformly arranged in respective electrodes, has the outgoing direction which is different from that of the diffracted light from the diffraction grating formed by the electrode pieces. Thus, the diffracted light by the density distribution of the particles can be selectively detected.
In accordance with the method and the apparatus proposed above, the intensity of the diffracted light from the diffraction grating resulting from the concentration distribution of the particles is detected, and thus the intensity is greater than that of scattered light from particles obtained in the dynamic scattering method, thereby a more intense signal is to be measured, resulting in a significant improvement in S/N and sensitivity relative to the dynamic scattering method.
The present inventors clarified that calculation for obtaining information about the diffusion coefficient and information about the particle size and the like from the temporal change in the diffracted light measured by the method based on the proposals above can be extremely simplified and also the information can be accurately obtained (refer to Non-patent Literature 1, for example).
That is, assuming that I represents the diffracted light intensity in the annihilation process of the diffraction grating resulting from the density distribution of the particles, I0 represents the starting value of the diffracted light intensity (immediately after the start of the annihilation), D represents the diffusion coefficient of the particles to be measured, and Λ represents the grating period, they are approximated by the following expressions (1) and (2).
                    [                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          1                ]                                                            I        =                              I            0                    ⁢                      exp            ⁡                          (                                                -                  2                                ⁢                                                                  ⁢                                  Dq                  2                                ⁢                t                            )                                                          (        1        )                                [                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          2                ]                                                            q        =                              2            ⁢                                                  ⁢            π                    Λ                                    (        2        )            
The size “d” of the particles to be measured can be obtained from the following Einstein-Stokes relational expression using such diffusion coefficient D obtained from the measured value I of the diffracted light intensity in the annihilation process of the diffraction grating. The viscosity η of the medium can also be obtained by using particles whose particle size “d” is known.
                    [                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          3                ]                                                            D        =                                            k              B                        ⁢            T                                3            ⁢                                                  ⁢            π            ⁢                                                  ⁢            η            ⁢                                                  ⁢            d                                              (        3        )            
In the expression (3), kB is the Boltzmann constant, and T represents an absolute temperature.
Patent Literature 1: U.S. Pat. No. 5,094,532
Patent Literature 2: Japanese Patent Laid-Open Publication No. 2001-159595
Patent Literature 3: Japanese Patent Laid-Open Publication No. 2006-84207
Patent Literature 4: WO/2007/010639
Non Patent Literature 1: “Nanoparticle size analysis with relaxation of induced grating by dielectrophoresis” Yukihisa Wada, Shinichro Totoki, Masayuki Watanabe, Naoji Moriya, Yoshio Tsunazawa, and Haruo Shimaoka, OPTICS EXPRESS, 12 Jun. 2006/vol. 14, No. 12, pp 5755-5764